Carbon Management Technology Conference,
7-9 February 2012,
Orlando, Florida, USA
This paper presents a graphical solution to model fluid flow in permeable media
in the presence of compressibility. Analytical solutions are important as
numerical simulations do not yield explicit expressions in terms of the model
parameters. Furthermore, simulations that provide the most comprehensive
solutions to multiphase flow problems are computationally intensive.
The method of characteristics (MOC) solution of the overall mass conservation
equation of CO2 in two-phase two-component flow through permeable media is
derived while considering the compressibility of fluids and the rock. The
previously developed MOC solutions rely on the incompressible fluid and rock
assumptions that are rarely met in practice; hence, the incompressible
assumption is relaxed and the first graphical/analytical solution for
compressible flow is derived. The analytical solution is validated by
The results suggest that the velocity of a wave, which is associated with the
transport of a certain mass of CO2 along the permeable medium, is a function of
compressibility of the rock and fluid, fractional flow terms, gas saturation,
and the slope of fractional flow curve. Furthermore, the wave velocity will be
only function of fractional flow terms, gas saturation, and the slope of
fractional flow curve if the compressibility of the rock is negligible compared
to that of CO2.
Thus, this paper explains how fast a compressible CO2 plume will travel along
the aquifers length. In practice, the fate of the injected CO2 plume is
essential to determine the storage capacity of aquifers and to evaluate the
risk associated with the CO2 sequestration projects.
Despite extensive research on analytical modeling of CO2 sequestration in
saline aquifers (Szulczewski et al., 2009; Juanes et al., 2010; Ghanbarnezhad
et al., 2011), the gas always has been considered as an incompressible fluid.
The method of characteristics (MOC) solution of the overall composition balance
equation of CO2 is derived for one-dimensional (1D) two-phase two-component
flow in the presence of compressibility. In the following study, the
incompressible assumption is relaxed as unequal injection and discharge rates
occur more often in practice; the unequal rates exhibit the compressibility of
fluids. Note that with zero compressibility involved, it is impossible to
inject more than the discharge rate in an aquifer. Thus, the total flow
velocity (gaseous +aqueous) stays constant with distance when compressibility
is absent; on the contrary, it can vary in the presence of compressibility; the
continuity equation necessitates this statement.